I have found that it will dutifully write the TIN to the folder that contains the fGDB (ie, the folder with the '.gdb' extension), but it is not actually part of the fGDB in the database sense.
It's rather dangerous behaviour, as nothing should ever touch those .gdb folders except ArcMap, as there is a danger of corrupting the database. It's crazy that ArcMap will just write other files there, where it cannot later see them (from Catalog, or ArcMap). It can read them initially, but you can't manually load them from there through ArcMap later.